Chapter IX: Part 9

Never have I found a more perfect description of that which I have termed criminal, epileptoid vertigo. But here again is a mistake of fact arising from a velleity not content with knowledge. It is that the novelist several times explains these bloodthirsty sexual instincts by a peculiar kind of atavism: the tendency, namely, to avenge the evil that women had done to his race; the spite accumulated from male to male since the first deceit in the depths of caverns. This is an error of fact. Primitive women have never done wrong to men. More feeble than men, they have always been their victims. These bloodthirsty sexual instincts are explained by a quite different atavism, which goes back to inferior animals, to the conflict between the males for the conquest of the female, who remained for the strongest; and by the blows that were inflicted on the woman in order to reduce her to conjugal slavery, conflicts of which traces still remain in Roman history (the Rape of the Sabines), and in the nuptial rites of almost all European countries, and in those of New Zealand, where the husband knocks down his wife before carrying her off to the matrimonial bed.

Another technical defect is, that a man who has arrived at the degree of degeneracy that Jacques has, ought to have still other vices: as great violence of character, impulsiveness without cause, profound immorality; while, as a matter of fact, except in moments of sexual fury, he appears as a good and honorable man. However, even recognising the force of his bloody sexual monomania, I find that instinctive aversion, characteristic of the good man, to be proper which Jacques feels at the thought of killing some one who is not a young and beautiful woman; for instance, to killing his rival, notwithstanding the favorable circumstances and the suggestions of Séverine.

"To kill that man, my God! Had he the right to do it? When a
fly troubled him he would crush it with a blow. One day when
a cat had got between his legs, he had broken its back with
a kick. But to kill this man, his fellow-creature! He must
reason with himself, he must prove his right to murder; the
right of the strong whom the weak are troublesome to.... But
afterwards that appeared to him monstrous, impracticable,
impossible. The civilised man revolted in him, the acquired
force of education, the slow and indestructible concretion of
inherited ideas. His cultivated brain, filled with scruples,
repelled murder with horror, as soon as he began to reason
about it. Yes, to kill in a case of necessity, in a transport
of rage! But to kill voluntarily by design, and from interest,
no never, never could he do it!"

All that is very true. Where the author has certainly copied after nature is in the personality of Séverine. She is not a true criminal; sensual, depraved though still young, experiencing love only in adultery. Though deceitful, she is nevertheless a good wife and a good housekeeper up to the day where chance had thrown her into evil doing. She is united to her husband, and for that reason she becomes his accomplice in crime, without horror or dread; but afterwards, seized with love for Jacques, she experiences dislike for her husband and wishes to turn the lover into his murderer.

"The need increased in her of having Jacques for herself,
all for herself, to live together, days and nights, without
ever more parting. Her hatred of her husband grew greater,
the mere presence of this man threw her into a morbid and
intolerable condition of excitement. Tractable, and with all
the amiability of a delicate woman, she became enraged at
everything in which he was concerned; she flew into a passion
at the least obstacle he put to her wishes.... The stupid
tranquillity in which she saw him, the indifferent glance
and manner with which he received her anger, his round back,
his enlarged stomach, all that greasy dullness which has the
appearance of happiness, made her exasperation complete. Oh!
to go far away from him.... One day when he returned, pale and
livid, to say that in passing before a locomotive he had felt
the buffer graze his elbow, she thought to herself that if
he were dead she would be free.... She would go with Jacques
to America.... She who at other times so rarely went out now
conceived a passion for going to see the steamships sail. She
would go to the pier, and would lean on her elbow watching
the smoke of the departing vessels.... [And at the decisive
moment] she threw herself passionately on Jacques's neck.
She fastened her burning lips to his. How she loved him and
how she hated the other! Oh! if she had dared, twenty times
already would she have done the deed ... but she felt herself
too gentle, it required the hand of a man. And this kiss which
would never come to an end, was all that she could communicate
to him of her courage, the full possession that she promised
him, the communion of her body. When she finally withdrew her
lips nothing more was left to her; she believed that she had
passed completely into him."

And is this, then, the woman criminal, the criminaloid, as I have called her (Vol. II of my "Uomo Delinquente")? A criminal who, when she is not urged onward by opportunities, (and these opportunities always have love for their origin,) is not capable of any true crime, and who when she commits it always makes use of the arm of another; and this latter is always her lover, for she finds herself too feeble to accomplish it herself. Her anatomical characters, as well as her physiognomy, if not those of the born criminal, have at least some features which those of other females have not, and which unite her with the animal. "She had very black and very thick hair, which stood like a helmet on her forehead, a long face, a strong mouth, and large blue-green eyes."

M. Héricourt justly finds that many features of this woman are to be met with in Gabrielle Fenayron, the accomplice of her husband. Gabrielle Fenayron is about thirty years of age: she is a tall dark woman with a very pale complexion; her hair is very black, the oval of her face elongated, and her eyes have a certain hardness that accentuate the projecting and unsightly cheek-bones. Gabrielle Fenayron, as we know, pretended to have been terrorised by the threats which her husband had uttered against her, and to have been infatuated, on the other hand, by the love that she felt for him; she had thus submitted her will in order to repair her fault. In the appreciation of this system of defence, the bill of indictment stated that the energy and the coolness exhibited by this woman in the preparation of assassination, the facilities that she had during the course of the long premeditation which had preceded the murder to warn Aubert without danger to herself, induced the belief that she had in the commission of the crime yielded to a profound hatred against her old lover. But this interpretation appears to me, psychologically, to be a clumsy and a forced one. It is not necessary to have recourse to motives left mysterious in order to explain the absolutely strange conduct of some women.

Perhaps Zola would have completed his picture if he had known Gabrielle Gompard; who allies and unites the passion of murder with prostitution when she attaches herself to a wicked man, but who grows animated for virtue and denounces herself an accomplice when she becomes the mistress of a virtuous man. These women change their personality in changing a lover, and then make a point of playing a role in the miserable world where their fickle passions destroy them.

Less happy, perhaps, has Zola been in the case of Flora, "fair, strong, with thick lips, and great greenish eyes, with low forehead set beneath heavy hair." According to the plot of the novel, she should be a criminal of passion. A good woman throughout her whole life, she commits a crime through jealousy. But the method of the crime (the derailment of a train with a view to striking her rival and her lover) is not that which is chosen by criminals of passion, who are unable to meditate long on their crimes, and who kill in day-light without premeditation. It is true that it is natural to the mind of female criminals to deal indirect and very complicated blows, and without proportion to the end to be attained: but all this is only the effect of their weakness. In a virago as strong as Flora is depicted, (a bellicose maid with the strong and hard arms of a boy,) this reason fails to satisfy us; and when she meditates her crime she is urged much less by thoughts of revenge, than by a necessity to commit the wrong in order to become cured of her own; she is then a born criminal, an epileptic rather than a creature of passion; and in this sense the attribute that he gives to Flora of a monstrous muscular force, that is observed very frequently in born criminals, would be reasonable. Thus the girl who always wore masculine clothes had a remarkable muscular power. Her weapon was a hammer, and with it she struck down many men.

I knew at Turin a murderess, a courtesan, who when a model in Paris, killed for money and love an artist, whose portrait she carried tattooed on her arm. This unfortunate woman fought two or three times with the five wardens of her prison. When liberated she was the head of all the scoundrels of Turin, challenging them to contest. One day even I found her in a red shirt, with epaulettes on. "It is my ensign," said she to me, "I am the captain of the scoundrels of Turin." But all these women are very different from Flora. Of course, a single and only love is wanting in their case.

It will finally be said, that the propensity which casts the two criminaloid women into the arms of the born criminal, the _bête humaine_, is copied from nature. As a matter of fact, there does exist a true elective affinity which unites the two sexes of these unfortunates; a cause that gives rise to criminal families, which form the nucleus of gangs. Nevertheless, the demonstration of it in this instance is not evident, for in crowding a large number of criminals into so narrow a space, great liberty of choice is excluded.

II.

CRIMINAL ANTHROPOLOGY AND PSYCHIATRY.

Secretions.—Dr. Ottolenghi[35] has made in my laboratory a number of observations with 15 born criminals and 3 occasional criminals, for the purpose of ascertaining the proportional quantities of urea, chlorides, and phosphates eliminated under the same alimentary conditions. Here are the average results:

GRAMMES.
Urea per 100 grammes of the weight {Born criminals 0·39
of the body {Occasional criminals 8·53

Phosphates do {Born criminals 0·024
{Occasional criminals 0·0195

Chlorides do {Born criminals 0·28
{Occasional criminals 0·29

[35] _Journal of the Medical Academy of Turin_, 1888, _Archiv.
di Psichiatria, Scienze penali ed Antropologia Criminale_,
Turin, 1888, x, Lombroso.

There is therefore amongst the born criminals a diminution in the elimination of urea; and an augmentation in that of phosphates, while the elimination of chlorides does not vary. He has obtained the same results in the case of psychical epilepsy; while the occasional criminal offers no anomaly.

In connection with this it may be stated, that, on the other hand, Mr. Rivano[36] found amongst epileptics on the days of paroxysm a greater quantity of urea and less phosphates.

[36] _Archiv. di Freniatria_, Turin, 1889.

Power of Smell.—Dr. Ottolenghi has also studied the power of smell amongst criminals. He has contrived with this object in view an osmometer, containing 12 aqueous solutions of the essence of cloves varying from 1 part in 50,000 to 1 part in 100. He made his observations in several series, one each day only; the conditions of ventilation being about the same, and the solutions being renewed for each observation, to avoid errors caused by evaporation. He looked first for the lowest degree at which olfactory perception began. In former experiments he proceeded differently. He disarranged the different bottles, and requested the subject to replace the same in the order of the intensity of their odor. He has divided the errors of disposition which resulted into serious and less serious errors, according as, in the order of the solutions, there occurred a distance of several or only one degree. He examined 80 criminals (50 men, 30 women) and 50 normal persons (30 men, mostly chosen amongst the prison warders, and 20 respectable women). Here are the results:

While amongst the normal males the average power of smell varied between the third and fourth degree of the osmometer, amongst the criminals it varied from the fifth to the sixth degree; 44 individuals had no power of smell at all. While the honest men made an average of three errors in the disposition of the bottles, the criminals made five, of which three were so-called serious ones.

The normal women touched the fourth degree of the osmometer, the criminal women the sixth degree; with two the power of smell was wanting entirely. While the normal women made an average of four faults in the disposition, the criminal women made five.

In eight cases of anosmia (loss of the sense of smell), presented in a certain set of criminals, two cases were due to nasal deformities; the others were a kind of smell-blindness; the subjects were susceptible to odoriferous excitations, but were unable to specify them and still less to classify them.

To verify what was really true in the assertion,[37] that criminal offenders against morality and customs have a highly developed power of smell, he examined this power in 30 ravishers and 40 prostitutes. In the former he found olfactory blindness in the ratio of 33 to 100; the remainder possessed an average power corresponding to the fifth degree of the osmometer. Arranging, then, the different solutions according to their intensity, he observed three so-called serious errors. In 19 per cent. of the girls submitted, he found olfactory blindness; and for the others an average acuteness corresponding to the fifth degree of the osmometer. Comparing these results with those obtained for the normal subjects and for regular criminals, the power of smell appears much less developed in the class just considered.

[37] Krafft-Ebing, _Psychopatia sexualis_, 4th ed., Stuttgart,
1889.—_Archiv. di Psichiatria_, 1889.

Taste.—Dr. Ottolenghi has also examined the sense of taste of 100 criminals (60 born criminals, 20 occasional criminals, and 20 criminal women). He compared them with 20 men taken from the lower classes, 20 professors and students, 20 respectable women, and 40 prostitutes. These series of experiments were made with 11 solutions of strychnine (graduated 1/80000 to 1/50000) and of saccharine (from 1/100000 to 1/10000), and 10 of chloride of sodium (1/500 to 3/100). The criminals showed remarkable obtuseness. The lowest degree of acuteness was found in the proportion of 38 to 100 in born criminals, 30 to 100 in occasional criminals, 20 to 100 in criminal women; while we found it in 14 per cent. of the professors and the students, in 25 per cent. of the men from the lower classes, in 30 per cent. of the prostitutes, and finally in 10 per cent. of the respectable women.

Walk.—A study which I have made with Perachia,[38] shows us that, contrary to the case of normal men, the step of the left foot of criminals is generally longer than that of the right; besides they turn off from the line of the axis more to the right than to the left; their left foot, on being placed on the ground, forms with this line an angle of deviation more pronounced than the angle formed by their right foot; all these characteristics are very often found among epileptics.

[38] _Sur la Marche suivant la Méthode de Gilles de la Tourette._

Gestures.—It is an ancient habit among criminals to communicate their thoughts by gestures. Avé-Lallemant describes a set of gestures used among German thieves,—a real language executed solely with the fingers, like the language of the deaf. Vidocq says that pickpockets, when they are watching a victim, give each other the signal of Saint John, which consists in putting their hand to their cravat or even in taking off their hat. But Pitré especially has published the most important information on this point. In his "Usi e Costumi della Sicilia" (Usages and Customs of Sicily,) he describes 48 special kinds of gestures employed by delinquents. This phenomenon is explained by the exaggerated mobility with which born criminals are endowed, as is the case with children.

MORPHOLOGICAL ANOMALIES.

The Skeleton.—Mr. Tenchini, having made studies upon 63 skeletons of criminals, has found in the proportion of 6 out of 100 cases, the perforation of the olecranon (the bony prominence at the back of the elbow) which one observes in 36 out of 100 Europeans, and in 34 out of 100 Polynesians; he likewise observed additional ribs and vertebræ in 10 cases out of 100 of them, and also too few, in the same proportion; which reminds us of the great variableness of these bones in the lower vertebrates. Lately he has even found in a criminal 4 sacral vertebræ too few, made up by 4 supplementary cervical vertebræ.

Madame Tarnorosky in her study of prostitutes, female thieves, and peasant women has demonstrated,[39] that the cranial capacity of prostitutes is inferior to that of female thieves and peasant women and particularly to that of women of good society;[40] _vice versa_, the zygomas (bones of the upper jaw) and the mandibles (lower jaw) were more developed among the prostitutes, who also exhibited a greater number of anomalies, in the proportion of 87 to 100, while the proportion of the female thieves showing anomalies was 79 to 100, and the proportion of peasant women was 12 to 100. The prostitutes had 33 in 100 of their parents addicted to drink, while the female thieves had 41 in 100 and the peasant women 16 in 100. Mr. De Albertis has found tattooing among 300 prostitutes of Genoa in the enormous proportion of 70 in 100.[41] He has also found the tactile sensibility of the women very much diminished: 3·6 millimetres to the right and 4 millimetres to the left.

[39]
50 100 100 50 50 50
PROSTITUTES. PROSTITUTES. FEMALE PEASANT PEASANT LADIES OF
MEASUREMENTS. THIEVES. WOMEN. WOMEN. GOOD
(NORTH.) (SOUTH.) SOCIETY.
Anteropost. diam. 17·7 17·8 17·9 18·3 18 18·3
Max. trans. diam. 13·9 14·4 14·9 14·5 14·5 14·5
Max. circumference 52·9 53·3 53·5 52·7 53·6 58·8
Zygomatic dist. 11·4 11·3 11·2 10·9 11·4 11·3
Mandib. biang.
distance 10·1 10·18 9·1 9·1 9·9 9·8

[40] _Archiv. di Psichiatria_, Mierjeivki, 1887.—Ibid., 1888,
p. 196.

[41] _Arch. di Psichiatria_, x, 1889.

Among criminal women, Saloalto has made studies altogether new; he has recognised among 130 female thieves the degenerative character, anomalies of the skull and of the physiognomy, in a less degree than among the men; he has found brachycephaly in 7, oxycephaly in 29, platycephaly in 7, the retreating forehead in 7, strabismus in 11, protruding ears in 6; the sense of touch was normal in 2 out of 100, the reflexions of the tendons decreasing in 4 out of 100, exaggerated in 12 out of 100.

Marro and Marselli have explained by sexual selection this enormous difference, which one also finds among epileptics and particularly in insane people; the men in fact do not choose ugly women with degenerative characters, while the women have no choice, and very often an ugly man, criminal, but vigorous, for this reason triumphs over all obstacles; sometimes he is even preferred. (Flaubert, "Correspondance," 1889.) Let us add that the cares of maternity soften the character of women, and augment in them the sentiment of pity.

Dr. Ottolenghi[42] has studied in my laboratory the wrinkles of 200 criminals and 200 normal persons (workingmen and peasants), and he has found that they occur earlier and much more frequently among the criminals; in fact, two to five times more so than among normal persons, with predominance of the zygomatic wrinkle (situated in the middle of each cheek), which wrinkle may well be called the wrinkle of vice, and is the characteristic wrinkle of criminals.

[42]
UNDER 25 YEARS. BETWEEN 25 AND 50 YEARS.
NORMAL. CRIMINAL. NORMAL. CRIMINAL.
LOCATION. p. 100. p. 100. p. 100. p. 100.

Wrinkles of the forehead 7·1 34 62 86
Nasolabial wrinkles 22 69 62 78
Zygomatic wrinkles 0 16 18 33

In criminal women (80) also, wrinkles have been found more frequent than in normal women, although here the difference is not so marked. One calls to mind at once the wrinkle of the sorcerers. It is enough to look at the bust of the celebrated Sicilian woman poisoner, preserved in the National Museum of Palermo, and whose face is one heap of wrinkles.

Dr. Ottolenghi, studying with me the frequency of canities (turning grey) and baldness in people, has demonstrated either absence or lateness of the same among criminals,[43] as also among epileptics and among cretins. Among the first, swindlers only tend to approach more the normal type.[44] On the other hand, among 280 criminal women canities was found more frequently, and baldness less frequently, than in the case of 200 honest workingmen.

[43] _La Calvizie, la Canizie e le Rughe nei normali,
nei criminali negli epiletis e nei cretini_. _Archiv. di
Psichiatria_, 1889, x.

[44]
CLASSES. WITH CANITIES. WITH BALDNESS.
p. 100. p. 100.

400 Normal people 62·5 19
80 Epileptics 31·5 12·7
40 Cretins 11·7 13·5
490 Criminals 25·9 48
Thieves 24·4 2·6
Swindlers 47 13·1
Maimers 23·7 5·3
80 Criminal women 45 9·7
200 Honest women 60 13

We shall not terminate this part of our discussion without making mention of the beautiful discovery that we owe—it pleases us to state—to a lawyer, Mr. Anfosso. The tachyanthropometer which he has constructed is a real automatic measurer. (Archiv. di Psych., Art. IX. p. 173.) We might name it,—if the word did not possess a little too much local color,—an anthropometric guillotine; so quickly and with the precision of a machine, does it give the most important measurements of the body, which makes the practice of anthropometry very easy, even to people who are entire strangers to the science; and it facilitates, moreover, the examination of the description of individual criminals, the perfection of which will always remain one of the most glorious distinctions of M. Bertillon. And at the same time that this instrument renders services to the administration of justice, it permits on a grand scale observations which hitherto were only obtainable by the learned.

Experiments were made a short time ago by Mr. Rossi, who studied the result of these measurements in 100 criminals (nearly all thieves). He found the breadth of the span of the arms to be greater than the height of body in 88; and in 11 to be less. In 30 he found the right foot larger; in 58 he found the left foot larger; in 12 both feet equal. The right arms of 43 per cent. were longer than the left, and the left in 54 per cent. longer than the right. Which confirms to a marvellous degree the _gaucherie_, mancinism, or structural misproportion, that had before been indicated by dynamometry and the study of the walk of criminals.[45]

[45] _Archiv. di Psichiatria_, 1889, Vol. x. p. 191.

The very frequent recurrence of anatomical misproportion and _gaucherie_ could not be better confirmed; and there are in this atavistic symptoms, for Rollet has observed in 42 anthropoids the left humerus to be longer than the right, in the proportion of 60 to 100, while among men the proportion is only 7 out of 100. (_Revue Scientifique_, 1889.)

This anatomical misproportion I have very recently verified with Mr. Ottolenghi by measurements of the two hands, the middle fingers, and the feet, right and left, in 90 normal persons and in 100 born criminals.[46] (Archiv. di Psichiatria, X. 8.)

[46]
HAND LONGER. MIDDLE FINGER. FOOT.
TYPES. RIGHT. LEFT. RIGHT. LEFT. RIGHT. LEFT.
PER CENTUM. PER CENTUM. PER CENTUM.

Normal persons 14·4 11 16·6 15·5 38·5 15·6
Criminals 5 25 10 27 27 35
Swindlers 4·3 13 13 21·7 21·7 26
Ravishers 7 14·2 14·2 28·4 35·7 35·7
Maimers 15 25 5 25 20 55
Thieves 0 34·8 13 30·4 26 26·6
Pickpockets 0 35 5 30 35 25

Tattooing.—I was under the belief that in this respect nothing more was to be said after the beautiful studies of Messrs. Lacassagne and Marro, and after my own.[47]

[47] See _Nouvelle Revue_; also my _Uomo Delinquente_, 4th ed., 1889.

However, the researches made by Messrs. Severi, Lucchini, and Boselli on 4,000 new criminals have given results of a high importance and first of all a proportion eight fold greater than that of the alienists of the same district (Florence and Lucca). The prevalency of this practice is enormous; it amounts to 40 in 100 among military criminals and to 33 in 100 among criminals under age; the women give a proportion of only 1·6 in 100, but this would be increased to 2 in 100 if we included certain kinds of fly-tattooing (_tatouages mouches_) resembling beauty spots, which are found even in high life prostitution.

What chiefly astonishes us in these researches, next to the frequency of the phenomena, is the specific character of the tattooings: their obscenity, the vaunting of crime, and the strange contrast of evil passions and the highest sentiments.

M. C..., aged 27 years, convicted at least fifty times for affrays, and the assaulting and wounding of men and horses, has the history of his crimes literally written on his skin; and in this respect, let us note that the infamous De Rosny, who only lately committed suicide in Lyons, had her body covered with tattooings in the form of erotic figures; one could read there the list of her lovers and the dates at which she left them.

F. L..., a carrier, aged 26 years, several times convicted, bears on his breast a heart pierced by a poniard (the sign of vengeance), and on his right hand a female singer of a _café chantant_, of whom he was enamoured. By the side of these tattooings, and others which propriety forbids us to cite,[48] one sees with surprise the picture of a tomb with the epitaph: "To my beloved father." Strange contradictions of the human mind!

[48] See _Atlas de L'Homme Criminel_. 1888. Alcan.

A certain B..., a deserter, has on his chest a St. George and the cross of the Legion of Honor, and on the right arm a woman, very little dressed, who drinks with the inscription: "Let us wet the interior a little."

Q. A..., a laborer, convicted many times for theft, expelled from France and Switzerland, has on his chest two Swiss gendarmes with the words "Long live the Republic!" On his right arm he has a heart pierced through, and at the side the head of a fish—a mackerel, to signify that he will poniard a bully, his rival.

We have seen on the left arm of another thief, a pot with a lemon tree, and the initials V. G. (_vengeance_); which in the strange language of the criminals means: treason, and, afterwards, revenge. He did not conceal from us the fact that his constant thought was to revenge himself on the woman who loved him and then abandoned him. His desire was to cut off her nose. His brother offered to perform the operation for him, but this he refused, reserving for himself the pleasure of executing his purpose when he should ultimately be liberated.

One sees, therefore, from these few examples, that there is among criminals a kind of hieroglyphical writing, but which is not regulated or fixed. The system is founded on daily happenings and slang, as would be the case among primitive mankind. Very often, in fact, a key signifies among thieves the silence of secrecy; and a death's-head (the bare skull), revenge. Sometimes points are used instead of figures. In this way one criminal marked himself with 17 points, which means, to his mind, that he proposes to inflict injury on his enemy seventeen times, whenever he meets with him.

The criminal tattooers of Naples have the habit of making long inscriptions on their bodies; but initials are used instead of words. Many Camorrists of Naples carry a tattooing which represents iron bars, behind which there is a prisoner and underneath the initials Q. F. Q. P. M.; which means: "Quando finiranno queste pene? Mai!" (When will these pains end? Never!) Others bear the epigraph C. G. P. V., etc., which means: "Courage, galeriens, pour voler et piler; nous devons tout mettre à sang et à feu!" (Courage, convicts, to steal and to rob; we must put all to the sword and fire!) We see here at once that certain forms of tattooing are employed by criminal federations, and serve as a sort of rallying-call. In Bavaria and in the South of Germany, the pickpockets, who are united together in real alliances, recognise each other by the epigraphic tattooing "T and L," which means _Thal und Land_ (valley and country); words which they must exchange in a low voice when they meet each other, in order not to be denounced to the police. A thief R..., who has on his right arm a design representing two hands crossed, and the word _union_ (unity) surrounded by a garland of flowers, told us that this tattooing is extensively adopted by malefactors in the South of France (Draguignan). According to the revelations made to us by emerited Camorrists, a lizard or a serpent denotes the first grade of this dangerous association.

I pass over in silence, and for good reasons, the tattooings spread over all the remaining parts of the body.

In the _Revista de Antropologia Criminal_, a new publication which has just appeared in Madrid, Mr. Sallilas has published an excellent study relative to the tattooing of Spanish criminals. According to him, this is a frequent custom among murderers. The predominance of the religious character is there noticeable, but always with the seal of lewd obscenity, universally observed. I have lately had occasion to verify up to what point the impulsion which leads criminals to inflict on themselves this strange operation, is atavistic. One of the most incorrigible thieves I have met, who has six brothers tattooed like himself, begged of me, notwithstanding he was half covered with the most obscene tattooings, to find him a professional tattooer who should complete what might well be called the carpeting of his skin. "When the tattooing is very odd and grotesque, and spreads over the whole body," he said, "it is for us thieves what the black dress coat and the decorated vest is to society. The more we are tattooed the greater is our esteem for one another; the more an individual is tattooed, the more authority has he over his companions. On the other hand, he who is not much tattooed enjoys no influence whatsoever with us; is not considered a thorough scoundrel, and has not the estimation of his fellows." "Very often," another told me, "when we visited prostitutes, and they saw us covered all over with tattooings, they overwhelmed us with presents, and gave us money instead of demanding it." If all that is not atavism, atavism does not exist in science.

Of this characteristic, of course, as of all the other characteristics of criminals, one may say that it is to be met with among normal people. But the chief thing here is its proportion, its commonness, and the exaggerated extent to which it is practised. Among honest, respectable people its peculiar complexion, its local and obscene coloring, and the useless, vain, and imprudent display of crime are wanting.

Again, it will probably be objected that this is not psychology, and that only through the latter science can we trace out the picture of the criminal. I could well answer here, that these tattooings are really psychological phenomena. And I may add that Mr. Ferri, in the introductory part of his work on Homicides, has given us in addition to a real statistical psychology, an analysis of all criminal propensities and of their extent before and after the crime.

Among born criminals, for example, 42 in 100 always deny the crime with which they are charged, while among occasional criminals, and in particular among maimers, only 21 in 100 deny all; of the first 1 in 100, and of the second 2 in 100 confess their crime with tears; etc.[49]

[49] _L'Omicidio_, Turin, 1890.

CESARE LOMBROSO.

[Prof. Lombroso has in preparation for this series of
criminological studies, an essay on the physiognomy of the
Anarchists.—ED.]

THE SQUARING OF THE CIRCLE.

AN HISTORICAL SKETCH OF THE PROBLEM FROM THE EARLIEST TIMES TO THE PRESENT DAY.[50]

[50] From Holtzendorff and Virchow's _Sammlung
gemeinverständlicher wissenschaftlicher Vorträge_, Heft 67.
Hamburg: Verlagsanstalt, etc.

I.

#Universal interest in the problem.#

For two and a half thousand years, both trained and untrained minds have striven in vain to solve the problem known as the squaring of the circle. Now that geometers have at last succeeded in giving a rigid demonstration of the impossibility of solving the problem with ruler and compasses, it seems fitting and opportune to cast a glance into the nature and history of this very ancient problem. And this will be found all the more justifiable in view of the fact that the squaring of the circle, at least in name, is very widely known outside of the narrow limits of professional mathematicians.

#The resolution of the French Academy.#

The Proceedings of the French Academy for the year 1775 contain at page 61 the resolution of the Academy not to examine from that time on, any so-called solutions of the quadrature of the circle that might be handed in. The Academy was driven to this determination by the overwhelming multitude of professed solutions of the famous problem, which were sent to it every month in the year,—solutions which of course were an invariable attestation of the ignorance and self-consciousness of their authors, but which suffered collectively from a very important error in mathematics: they were _wrong_. Since that time all professed solutions of the problem received by the Academy find a sure haven in the waste-basket, and remain unanswered for all time. The circle-squarer, however, sees in this high-handed manner of rejection only the envy of the great towards his grand intellectual discovery. He is determined to meet with recognition, and appeals therefore to the public. The newspapers must obtain for him the appreciation that scientific societies have denied. And every year the old mathematical sea-serpent more than once disports itself in the columns of our papers, that a Mr. N. N., of P. P., has at last solved the problem of the quadrature of the circle.

#General ignorance of quadrators.#

But what kind of people are these circle-squarers, when examined by the light? Almost always they will be found to be imperfectly educated persons, whose mathematical knowledge does not exceed that of a modern college freshman. It is seldom that they know accurately what the requirements of the problem are and what its nature; they never know the two and a half thousand years' history of the problem; and they have no idea whatever of the important investigations and results which have been made with reference to the problem by great and real mathematicians in every century down to our time.

#A cyclometric type.#

Yet great as is the quantum of ignorance that circle-squarers intermix with their intellectual products, the lavish supply of conceit and self-consciousness with which they season their performances is still greater. I have not far to go to furnish a verification of this. A book printed in Hamburg in the year 1840 lies before me, in which the author thanks Almighty God at every second page that He has selected him and no one else to solve the 'problem phenomenal' of mathematics, "so long sought for, so fervently desired, and attempted by millions." After the modest author has proclaimed himself the unmasker of Archimedes's deceit, he says: "It thus has pleased our mother nature to withhold this mathematical jewel from the eye of human investigation, until she thought it fitting to reveal truth to simplicity."

This will suffice to show the great self-consciousness of the author. But it does not suffice to prove his ignorance. He has no conception of mathematical demonstration; he takes it for granted that things are so because they seem so to him. Errors of logic, also, are abundantly found in his book. But apart from this general incorrectness let us see wherein the real gist of his fallacy consists. It requires considerable labor to find out what this is from the turgid language and bombastic style in which the author has buried his conclusions. But it is this. The author inscribes a square in a circle, circumscribes another about it, then points out that the inside square is made up of four congruent triangles, whereas the circumscribed square is made up of eight such triangles; from which fact, seeing that the circle is larger than the one square and smaller than the other, he draws the bold conclusion that the circle is equal in area to six such triangles. It is hardly conceivable that a rational being could infer that something which is greater than 4 and less than 8 must necessarily be 6. But with a man that attempts the squaring of the circle this kind of ratiocination _is_ possible.

Similarly in the case of all other attempted solutions of the problem, either logical fallacies or violations of elementary arithmetical or geometrical truths may be pointed out. Only they are not always of such a trivial nature as in the book just mentioned.

Let us now inquire whence the inclination arises which leads people to take up the quadrature of the circle and to attempt to solve it.

#The allurements of the problem.#

Attention must first be called to the antiquity of the problem. A quadrature was attempted in Egypt 500 years before the exodus of the Israelites. Among the Greeks the problem never ceased to play a part that greatly influenced the progress of mathematics. And in the middle ages also the squaring of the circle sporadically appears as the philosopher's stone of mathematics. The problem has thus never ceased to be dealt with and considered. But it is not by the antiquity of the problem that circle-squarers are enticed, but by the allurement which everything exerts that is calculated to raise the individual out of the mass of ordinary humanity, and to bind about his temples the laurel crown of celebrity. It is ambition that spurred men on in ancient Greece and still spurs them on in modern times to crack this primeval mathematical nut. Whether they are competent thereto is a secondary consideration. They look upon the squaring of the circle as the grand prize of a lottery that can just as well fall to their lot as to that of any other. They do not remember that—

"Toil before honor is placed by sagacious decrees of Immortals,"

and that it requires years of continued studies to gain possession of the mathematical weapons that are indispensably necessary to attack the problem, but which even in the hands of the most distinguished mathematical strategists have not sufficed to take the stronghold.

#About the only problem known to the lay world.#

But how is it, we must further ask, that it happens to be the squaring of the circle and not some other unsolved mathematical problem upon which the efforts of people are bestowed who have no knowledge of mathematics yet busy themselves with mathematical questions? The question is answered by the fact that the squaring of the circle is about the only mathematical problem that is known to the unprofessional world,—at least by name. Even among the Greeks the problem was very widely known outside of mathematical circles. In the eyes of the Grecian layman, as at present among many of his modern brethren, occupation with this problem was regarded as the most important and essential business of mathematicians. In fact they had a special word to designate this species of activity; namely, τετραγωνίζειν, which means to busy one's self with the quadrature. In modern times, also, every educated person, though he be not a mathematician, knows the problem by name, and knows that it is insolvable, or at least, that despite the efforts of the most famous mathematicians it has not yet been solved. For this reason the phrase "to square the circle," is now used in the sense of attempting the impossible.

#Belief that rewards have been offered.#

But in addition to the antiquity of the problem, and the fact also that it is known to the lay world, we have yet a third factor to point out that induces people to take up with it. This is the report that has been spread abroad for a hundred years now, that the Academies, the Queen of England, or some other influential person, has offered a great prize to be given to the one that first solves the problem. As a matter of fact we find the hope of obtaining this large prize of money the principal incitement to action with many circle-squarers. And the author of the book above referred to begs his readers to lend him their assistance in obtaining the prizes offered.

#The problem among mathematicians.#

Although the opinion is widely current in the unprofessional world, that professional mathematicians are still busied with the solution of the problem, this is by no means the case. On the contrary, for some two hundred years, the endeavors of many considerable mathematicians have been solely directed towards demonstrating with exactness that the problem is insolvable. It is, as a rule,—and naturally,—more difficult to prove that something is impossible than to prove that it is possible. And thus it has happened, that up to within a few years ago, despite the employment of the most varied and the most comprehensive methods of modern mathematics, no one succeeded in supplying the wished-for demonstration of the problem's impossibility. At last, Professor Lindemann, of Königsberg, in June, 1882, succeeded in furnishing a demonstration,—and the first demonstration,—that it is impossible by the exclusive employment of ruler and compasses to construct a square that is mathematically exactly equal in area to a given circle. The demonstration, naturally, was not effected with the help of the old elementary methods; for if it were, it would surely have been accomplished centuries ago; but methods were requisite that were first furnished by the theory of definite integrals and departments of higher algebra developed in the last decades; in other words it required the direct and indirect preparatory labor of many centuries to make finally possible a demonstration of the insolvability of this historic problem.

Of course, this demonstration will have no more effect than the resolution of the Paris Academy of 1775, in causing the fecund race of circle-squarers to vanish from the face of the earth. In the future as in the past, there will be people who know nothing, and will not want to know anything of this demonstration, and who believe that they cannot help but succeed in a matter in which others have failed, and that just they have been appointed by Providence to solve the famous puzzle. But unfortunately the ineradicable passion of wanting to solve the quadrature of the circle has also its serious side. Circle-squarers are not always so self-contented as the author of the book we have mentioned. They often see or at least divine the insuperable difficulties that tower up before them, and the conflict between their aspirations and their performances, the consciousness that they want to solve the problem but are unable to solve it, darkens their soul and, lost to the world, they become interesting subjects for the science of psychiatry.

II.

#Nature of the problem. Numerical rectification.#

If we have a circle before us, it is easy for us to determine the length of its radius or of its diameter, which must be double that of the radius; and the question next arises to find the number that represents how many times larger its circumference, that is the length of the circular line, is than its radius or its diameter. From the fact that all circles have the same shape it follows that this proportion will always be the same for both large and small circles. Now, since the time of Archimedes, all civilised nations that have cultivated mathematics, have called the number that denotes how many times larger than the diameter the circumference of a circle is, π,—the Greek initial letter of the word periphery. To compute π, therefore, means to calculate how many times larger the circumference of a circle is than its diameter. This calculation is called "the numerical rectification of the circle."

#The numerical quadrature.#

Next to the calculation of the circumference, the calculation of the superficial contents of a circle by means of its radius or diameter is perhaps most important; that is, the computation of how much area that part of a plane which lies within a circle measures. This calculation is called the "numerical quadrature." It depends, however, upon the problem of numerical rectification; that is, upon the calculation of the magnitude of π. For it is demonstrated in elementary geometry, that the area of a circle is equal to the area of a triangle produced by drawing in the circle a radius, erecting at the extremity of the same a tangent,—that is, in this case, a perpendicular,—cutting off upon the latter the length of the circumference, measuring from the extremity, and joining the point thus obtained with the centre of the circle. But it follows from this that the area of a circle is as many times larger than the square upon its radius as the number π amounts to.

#Constructive rectification and quadrature.#

The numerical rectification and numerical quadrature of the circle based upon the computation of the number π, are to be clearly distinguished from problems that require a straight line equal in length to the circumference of a circle, or a square equal in area to a circle, to be _constructively_ produced out of its radius or its diameter; problems which might properly be called "constructive rectification" or "constructive quadrature." Approximately, of course, by employing an approximate value for π these problems are easily solvable. But to solve a problem of construction, in geometry, means to solve it with mathematical exactitude. If the value π were exactly equal to the ratio of two whole numbers to one another, the constructive rectification would present no difficulties. For example, suppose the circumference of a circle were exactly 3-1/7 times greater than its diameter; then the diameter could be divided into seven equal parts, which could be easily done by the principles of planimetry with ruler and compasses; then we would produce to the amount of such a part a straight line exactly three times larger than the diameter, and should thus obtain a straight line exactly equal to the circumference of the circle. But as a matter of fact, and as has actually been demonstrated, there do not exist two whole numbers, be they ever so great, that exactly represent by their proportion to one another the number π. Consequently, a rectification of the kind just described does not attain the object desired.

It might be asked here, whether from the demonstrated fact that the number π is not equal to the ratio of two whole numbers however great, it does not immediately follow that it is impossible to construct a straight line exactly equal in length to the circumference of a circle; thus demonstrating at once the impossibility of solving the problem. This question is to be answered in the negative. For there are in geometry many sets of two lines of which the one can be easily constructed from the other, notwithstanding the fact that no two whole numbers can be found to represent the ratio of the two lines. The side and the diagonal of a square, for instance, are so constituted. It is true the ratio of the latter two magnitudes is nearly that of 5 to 7. But this proportion is not exact, and there are in fact no two numbers that represent the ratio exactly. Nevertheless, either of these two lines can be easily constructed from the other by the sole employment of ruler and compasses. This might be the case, too, with the rectification of the circle; and consequently from the impossibility of representing π by the ratio between two whole numbers the impossibility of the problem of rectification is not inferable.

The quadrature of the circle stands and falls with the problem of rectification. This is based upon the truth above mentioned, that a circle is equal in area to a right-angled triangle, in which one side is equal to the radius of the circle and the other to the circumference. Supposing, accordingly, that the circumference of the circle were rectified, then we could construct this triangle. But every triangle, as is taught in the elements of planimetry, can, with the help of ruler and compasses be converted into a square exactly equal to it in area. So that, therefore, supposing the rectification of the circumference of a circle were successfully performed, a square could be constructed that would be exactly equal in area to the circle.

The dependence upon one another of the three problems of the computation of the number π, of the quadrature of the circle, and its rectification, thus obliges us, in dealing with the history of the quadrature, to regard investigations with respect to the value of π and attempts to rectify the circle as of equal importance, and to consider them accordingly.

#Conditions of the geometrical solution.#

We have used repeatedly in the course of this discussion the expression "to construct with ruler and compasses." It will be necessary to explain what is meant by the specification of these two instruments. When such a number of conditions is annexed to a requirement in geometry to construct a certain figure that the construction only of _one_ figure or a limited number of figures is possible in accordance with the conditions given; such a complete requirement is called a problem of construction, or briefly a problem. When a problem of this kind is presented for solution it is necessary to reduce it to simpler problems, already recognised as solvable; and since these latter depend in their turn upon other, still simpler problems, we are finally brought back to certain fundamental problems upon which the rest are based but which are not themselves reducible to problems less simple. These fundamental problems are, so to speak, the undermost stones of the edifice of geometrical construction. The question next arises as to what problems may be properly regarded as fundamental; and it has been found, that the solution of a great part of the problems that arise in elementary planimetry rests upon the solution of only five original problems. They are:

1. The construction of a straight line which shall pass through two given points.

2. The construction of a circle the centre of which is a given point and the radius of which has a given length.

3. The determination of the point that lies coincidently on two given straight lines extended as far as is necessary,—in case such a point (point of intersection) exists.

4. The determination of the two points that lie coincidently on a given straight line and a given circle,—in case such common points (points of intersection) exist.

5. The determination of the two points that lie coincidently on two given circles,—in case such common points (points of intersection) exist.

For the solution of the three last of these five problems the eye alone is needed, while for the solution of the two first problems, besides pencil, ink, chalk, and the like, additional special instruments are required: for the solution of the first problem a ruler is most generally used, and for the solution of the second a pair of compasses. But it must be remembered that it is no concern of geometry what mechanical instruments are employed in the solution of the five problems mentioned. Geometry simply limits itself to the presupposition that these problems are solvable, and regards a complicated problem as solved if, upon a specification of the constructions of which the solution consists, no other requirements are demanded than the five above mentioned. Since, accordingly, geometry does not itself furnish the solution of these five problems, but rather exacts them, they are termed _postulates_.[51] All problems of planimetry are not reducible to these five problems alone. There are problems that can be solved only by assuming other problems as solvable which are not included in the five given; for example, the construction of an ellipse, having given its centre and its major and minor axes. Many problems, however, possess the property of being solvable with the assistance solely of the five postulates above formulated, and where this is the case they are said to be "constructible with ruler and compasses," or "elementarily" constructible.